Ariel is making flower arrangements. He has 7 roses and 14 daisies. If Ariel wants to make all the arrangements identical and have no flowers left over, what is the greatest number of flower arrangements that he can make?
What is the greatest common factor of 7 and 14?
To determine the maximum number of flower arrangements Ariel can make, we need to find the greatest common divisor (GCD) of the number of roses and daisies.
The GCD represents the largest number that can divide both the number of roses and daisies without leaving a remainder, which corresponds to the number of identical flower arrangements Ariel can create.
To find the GCD, we can use the Euclidean algorithm.
1. Begin by dividing the larger number (14) by the smaller number (7).
- 14 รท 7 = 2 with a remainder of 0.
2. Since the remainder is 0, the GCD is the smaller number (7).
- GCD(7, 14) = 7.
Therefore, Ariel can create a maximum of 7 identical flower arrangements using his 7 roses and 14 daisies.